i say the first light is the only one left on if you think about it, it works...
...not exactly...light 4 will definitely remain on.
after the first pass, with every other light it's turned on.
after the second pass it's turned off
on the third pass it remains untouched
the fourth pass turns it back on, and it's never touched again.
Light 4 is one of the lights that stays on.
Lot's of these lights will be toggled many times.
Given that I can't use scratch paper, are there any other resources that I may use too look at? Maybe some sort of standard tool used in grade school?
If I may, I have the answer, if not...well then, I still have the answer, but I won't submit it.
Here are the results. I wrote a script to out put the results. You can still show the math required to get the final line with skipping the previous 99 lines.
Yeah...that's what I came up with too. But I did it in my head...sort of.
After doing a few in my head, I realized that any number with an even number of factor sets, would remain off, I checked a multiplication table to see what numbers would have an odd number of factor pairs. Then it slapped me in the face when I saw the diagonal line of perfect squares down the middle.
You got it first Kong. Good job. This was an easy one if you wrote it out but that wasn't the challenge. The real challenge was how to approach it where you could solve it in your head. If you approach the problem focusing on one bulb at a time its very solvable, especially when you notice the pattern.
Ray: Back in the old days when my brother used to work, my brother used to have his wife drive him to the train station and then he'd take the train and go to work. Right after lunch he'd get to the train station and his wife would meet him there and they'd drive home. Well one day, he decides to leave work early at 11 am. Needless to say, he gets to the train station an hour early. Rather than call his wife, it's a nice day and he decides to hoof it. So he starts walking in the direction she'll be driving. And low and behold, he sees his wife coming up the road and she sees him by the side of the road taking a haircut. They get in the car and they drive home and arrive 20 minutes earlier. Don't forget - she left home at the usual time.
Tom: Of course, she didn't know he was going to leave work an hour early.
Ray: They get home 20 minutes earlier than they would have gotten home. How long was he walking before they met? Notice, there's no mention of how long she was driving, how fast he walked, what train he took, and what any other the distances were. How long was he walking before she picked him up?
Take a haircut:to accept a valuation or return that is less than optimal.
It's slang, basically It's just pointing out that he might have gotten out of work an hour early but he had to either wait around an hour or start walking because of it.
Needless to say, it has no relevance to the problem or the answer.
Ray: Back in the old days when my brother used to work, my brother used to have his wife drive him to the train station and then he'd take the train and go to work. Right after lunch he'd get to the train station and his wife would meet him there and they'd drive home. Well one day, he decides to leave work early at 11 am. Needless to say, he gets to the train station an hour early. Rather than call his wife, it's a nice day and he decides to hoof it. So he starts walking in the direction she'll be driving. And low and behold, he sees his wife coming up the road and she sees him by the side of the road taking a haircut. They get in the car and they drive home and arrive 20 minutes earlier. Don't forget - she left home at the usual time.
Tom: Of course, she didn't know he was going to leave work an hour early.
Ray: They get home 20 minutes earlier than they would have gotten home. How long was he walking before they met? Notice, there's no mention of how long she was driving, how fast he walked, what train he took, and what any other the distances were. How long was he walking before she picked him up?
At first glance I don't see how you can nail this down without knowing how fast either of them were going, or at least a ratio of their speeds (she traveled 10x faster) but I'll try a guess.
Both answers are wrong. There is a way to compute this mathematically. There's no "trick" to this, just finding a way to approach the problem correctly.
Solve for X
Pick up time at train station = T = 12
Wife departure time = D
Arrive at house time = A
Saved drive time = S = 20
Pick up time at road side = R
Start walking time = W = 11
Time walking = X
T - D = A - T
R - D = A - S - R
R - W = X
Known values filled in:
12 - D = A - 12
R - D = A - 20 - R
R - 11 = X
While your letters and numbers are fun to read, you still haven't answered the question Big D. How long was he walking for?
Like I said about the lightbulb question, you need to approach these differently. It's not about the solution, it's about rearranging your thought process.
WARNING: The answer is in here so don't read it if you want to figure it out on your own.
( Click to show/hide )
Because if they arrived home 20 mintues earlier than usual, he saved by walking 10 minutes of her travel time to the station and 10 minutes of her travel time from the station. Therefore, he was walking for 50 minutes when she picked him up. You have to put all of the pieces together. He left an hour earlier but she left at the same time and saves 20 minutes off the total trip. It's as if he moved the station 10 minutes closer. (10 + 50 = 60, 10 + 10 = 20)
_________________________________________________ Everyone knows that from planet Earth, the moon and sun appear to be about the same size, even though we know they're not the same size (from our vantage point they're the same size) hence we can get things like eclipses. The moon can go between us and the sun and block out the sun and if they didn't appear to be the same size we wouldn't have an eclipse. Now, knowing this, you can take the tip of your finger and at arms length you close one eye and you can block out the sun with the tip of your index finger. However, you go out at night and you hold that same finger up and close one eye and you can't block out the moon. How come?
You think the Moon appears larger when its near the horizon because you have things in the foreground to compare it with. That wouldn't effect the finger trick.
P.S. The horizon optical illusion also effects the Sun.
You think the Moon appears larger when its near the horizon because you have things in the foreground to compare it with. That wouldn't effect the finger trick.
P.S. The horizon optical illusion also effects the Sun.
So am I also correct in thinking that the whole, "finger at arm's length won't block out the moon" thing isn't always correct?
Are you saying that my finger isn't actually bigger at the horizon as well?
Is the answer that since the moon's orbital path is elliptical, it is closer to the earth at certain times, and as such appears bigger at these times?
Quote:
Originally Posted by TrakMastaTom
15 minutes?
We're past this. Click tenser's spoiler above for the answer.
So am I also correct in thinking that the whole, "finger at arm's length won't block out the moon" thing isn't always correct?
Are you saying that my finger isn't actually bigger at the horizon as well?
Is the answer that since the moon's orbital path is elliptical, it is closer to the earth at certain times, and as such appears bigger at these times?
1) It will always be correct under normal nocturnal circumstances. You can alter the test in a way to make it work but you would have to intentionally go out of your way to do it.
2) I'm saying that the answer has nothing to do with the horizon optical illusion and that the fact that the same thing happens to the Sun as well makes the point mute anyhow.
3) The ebb and neap of the Moon's elliptical orbit is not sufficient enough to effect this. This point is also mute because the Earth's orbit is elliptical to the Sun as well.
if you think about it, it works...
Linear Mode
